The dots in the expressions above denote the terms at the negative powers of \(\tilde{m}\)  or the positive powers of \(\beta \) . The coefficients diverging at \(\beta \rightarrow 0\)  provide the energy-time anomaly ([1]} and also [2]}, [3]}) when the energy cutoff is used for the regularization of the one-loop contribution to the effective action. Recall that the energy-time anomaly represents the variance of the renormalized effective action under the uniform dilatations of the Killing vector (see below). The flat spacetime limit of the expansions (REF ) and (REF ) coincides with the known one [4]}, [5]}, [6]}.
